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The definitions of AP and WAP were originated in categorical topology by A. Pultr and A. Tozzi, Equationally closed subframes and representation of quotient spaces, Cahiers Topologie Géom. Différentielle Catég. 34 (1993), no. 3, 167-183. In general, we have the implications: $T_2\Rightarrow KC\Rightarrow US\Rightarrow T_1$, where $KC$ is defined as the property that every compact subset is closed and $US$ is defined as the property that every convergent sequence has at most one limit. And a space is called submaximal if every dense subset is open....